\textbf{122.} The figure shows the graph of the function with the formula $f(x) = \dfrac{a\sin 2x + b}{\sin x + \cos x}$, which has period one. What is $a$?
\textit{[Figure: Graph of a periodic function with amplitude 2]}
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(1) $-1$ \hfill (3) $\sqrt{2}$ \\
(4) $2$ \hfill (1) $1$
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